A boundary integral technique for modelling two-phase flow in porous media

In this dissertation, particular attention is directed towards the development of a computationally tractable numerical technique applicable to the initial invasion of a denser than water phase into an initially pristine aquifer. This work applies a novel boundary integral formulation to the flow of two incompressible fluids in a porous medium. The usual boundary element assumption of piston-like flow is relaxed to include the effects of variable saturation on saturation-dependent phase properties, such as relative permeabilities and capillary pressures. The proposed technique may be considered a multiple-front formulation; unlike previous multiple-front formulations, however, capillary pressure effects are accommodated. The formulation straightforwardly accommodates problems where dispersive effects are small or negligible; such problems cause traditional methods great difficulty.; The proposed boundary integral technique places the computational mesh on selected saturation contours. As capillary pressure is considered a function of saturation, capillary pressure gradients can be considered a function of the saturation gradients; the gradient of saturation is determined by a separate boundary integral interpolation step, where the region between each pair of saturation contours is considered separately. Once the saturation field (and thus capillary pressure field) is calculated, the pressure distribution is determined using a multiple zone boundary integral formulation of the total flow equation, in which an effective saturation is used between each pair of contours to determine the saturation-dependent properties. Finally, time-stepping is performed by updating the location of the contours, based on the fluxes calculated from the pressure distribution, using a locally one-dimensional front-moving algorithm.; As the method requires that the contours change position over time, various mesh maintenance and mesh movement algorithms are evaluated. Specific attention is directed to the mesh movement algorithms in the important special case of a piston-like flow. With these results in hand, the formulation is compared against various two-phase analytic solutions, and a finite element simulator. Based on these examples, it is concluded that the method provides a viable new approach to simulating the invasion of a separate fluid phase into an aquifer.